The chances of events happening as determined by calculating results that would occur under ideal circumstances. For example, the theoretical probability of rolling a 4 on a four-sided die is 1/4 or 25%, because there is one chance in four to roll a 4, and under ideal circumstances one out of every four rolls would be a 4. Contrast with experimental probability (cf Probability and Outcome Discussion).

A theory of probability is a way of understanding probability statements. That is, a theory of probability connects the mathematics of probability, which is the set of consequences of the axioms of probability, with the real world of observation and experiment. There are several common theories of probability. According to the frequency theory of probability, the probability of an event is the limit of the percentage of times that the event occurs in repeated, independent trials under essentially the same circumstances. According to the subjective theory of probability, probability is a number that measures how strongly we believe an event will occur. The number is on a scale of 0% to 100% (or 0 to 1), with 0% indicating that we are completely sure it won't occur, and 100% indicating that we are completely sure that it will occur. See frequency view and personal view.